Modified Newtonian dynamics (MOND) is an empirically- motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to the widespread existence of cosmic dark matter. The basic idea is that at accelerations below about 1 angstrom per second squared, the effective gravitational acceleration approaches a specific non-Newtonian form. Over the past 20 years an impressive body of astronomical evidence in support of this idea has emerged. Here I review this evidence, discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics, and comment upon likely cosmological consequences.